In a large-scale Multiple-Input Multiple-Output (MIMO) or massive MIMO system, the BS is equipped with tens to several hundreds of transmitting antennas. It has received enormous attention due to its capability to provide linear capacity growth without the need of increased power or bandwidth. This is realized by employing Multi-User MIMO (MU-MIMO) to serve multiple UEs simultaneously in the same Resource Blocks (RBs). In this system, the BS groups UEs at each scheduling slot and transmits data to them on the same time and frequency resource. In order to remove the mutual interference among these UEs and maximize the multi-user sum rate, the BS needs to know the CSI in the downlink and the Channel Quality Information (CQI) of each UE in particular. However, it is infeasible to obtain the CSI directly by sending reference pilots in the downlink because of two reasons: 1. the large number of antennas would cause a very large system overhead for reference signals in the downlink; 2. A larger number of bits is needed to quantize the CSI accurately, which would cause overload of the feedback channel in the uplink. As a result, the reciprocal property of a wireless channel, such as in a TDD system or in an FDD system using switching to create channel reciprocity between the uplink and downlink as described in our patent application PCT/US14/71752, can be employed to reduce the reference signal overhead. In such a system, a UE sends a Sounding Reference Signal (SRS) to the BS in the uplink. The BS then estimates the uplink CSI through the received SRSs and uses it to estimate the downlink CSI based on channel reciprocity.